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Programming Enigma Puzzles

3 December 2011

Posted by on **From New Scientist #2831, 24th September 2011** [link]

My local football league has five teams, which each play each of the other teams twice. Three points are given for a win, and 1 point for a draw. At the end of the season, all five teams tied with the same number of points, so they were ordered by goal difference, which gave a clear winner. The team that drew the most games also won a game against the team that came top of the league.

How many games did the team that came top of the league win, draw and lose?

[enigma1665]

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The following Python code runs in 31ms.

From looking at the result(s) the team with the most draws (1w7d0l) also won a game against the team at the top of the league.

Since they have 7 draws and 1 win that means they have 2 draws against each of the teams with 2w4d2l and 1w1d against the team with 3w1d4l which must be the team at the top of the league.

Solution:The team at the top of the league won 3 games, drew 1 game and lost 4 games.